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rluce / tlcomp

Computing with Toeplitz and Toeplitz-like matrices in Matlab
MIT License
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Obtain 2-norm estimates from generator #17

Closed rluce closed 6 years ago

rluce commented 6 years ago

At every recompression we obtain the |GB'|_2 for free. Since |A|_2 <= sqrt(n) * |GB'|_2, this gives a good norm estimate at zero computational overhead.

rluce commented 6 years ago

While it is true that the norm can be obtained for free at each generator compression, this is a side effect that is not properly integrated into the logic. For example, there is no guarantee that gencompress() is called after every operation that modifies it.

A proper solution would be to represent the generator by a triple U S V, where S are the singular values and U,V are unitary.

For now we should implement a solution without side effects, explicitly recomputing the qr factorizations of G and B.